We present a complete list of the dimension-eight operator basis in standard model effective field theory using group theoretic techniques systematic and automated way. adopt new form operators terms irreducible representations Lorentz identify structures as states $SU(N)$ group. In this way, redundancy from equations motion is absent that integration by part treated fact independent forms an invariant subspace also decompose into ones with definite permutation symmetries among flavor...

We present a complete and independent list of the dimension-nine operator basis in Standard Model effective field theory by an automatic algorithm based on amplitude-operator correspondence. A ($Y$-basis) is first constructed enumerating Young tableau auxiliary $SU(N)$ group gauge groups, with equation-of-motion integration-by-part redundancies all removed. In presence repeated fields, another ($P$-basis) explicit flavor symmetries among them derived from $Y$-basis, which further induces...

A bstract We present a complete and independent off-shell Green’s basis of the dimension 8 operators in Standard Model effective field theory (SMEFT). propose an amplitude formalism such that this new kind has one-to-one correspondence to general carrying all kinds redundancies. The advantage is redundancies can be formulated explicitly terms spinors thus removed systematically from exhaustive list amplitudes. Following procedures, redundant reduced ones with only redundancy equation motion...

We obtain the complete and independent bases of effective operators at mass dimension 5, 6, 7, 8, 9 in both standard model field theory with light sterile right-handed neutrinos ($\nu$SMEFT) low energy ($\nu$LEFT). These theories provide systematical parametrizations on all possible Lorentz-invariant physical effects involving Majorana/Dirac neutrinos, with/without lepton number violations. In $\nu$SMEFT, we find that there are 2 (18), 29 (1614), 80 (4206), 323 (20400), 1358 (243944)...

Finding all possible UV resonances of effective operators is an important task in the bottom-up approach field theory. We present tree-level for dimension-5, -6, and -7 Standard Model theory (SMEFT) then obtain correspondence between from relations among their Wilson coefficients, through functional matching operator reduction procedure. This provides a cross-dimension UV/IR dictionary SMEFT at tree level, methods used here, especially on shell construction general Lagrangian systematic...

A bstract We construct the on-shell amplitude basis and corresponding effective operators for generic modified gravity theory, such as pure with higher derivatives, scalar-tensor gravity, Einstein-Yang-Mills, etc. Taking Weyl tensor building block, we utilize Young technique to obtain independent operators, without equation of motion total derivative redundancies. update our algorithm vastly increase speed finding monomial (m-basis) expressed in terms tensors Lorentz indices, familiar form...

We describe a general procedure to construct the independent and complete operator bases for generic Lorentz invariant effective field theories, given any kind of gauge symmetry content, up mass dimension. By considering as contact on-shell amplitude, so-called amplitude correspondence, we provide unified construction flavor structures by Young Tableau tensor. Several are constructed emphasize different aspects: independence (y-basis m-basis), repeated fields with flavors (p-basis),...

A bstract In the effective field theory (EFT), positivity bound on dim-8 operators tells us that s 2 contribution in scattering amplitude of 2-to-2 process geometrically corresponds to convex cone composed ultraviolet (UV) states as extremal rays. The J-Basis method can provide a complete group decomposition direct product gauge and Lorentz group, thus search for all UV states. Compared previous methods, which only perform groups, greatly improves strictness restrictions also provides...

A bstract We obtain the complete operator bases at mass dimensions 5, 6, 7, 8, 9 for low energy effective field theory (LEFT), which parametrize various physics effects between QCD scale and electroweak scale. The independence of basis regarding equation motion, integration by parts flavor relations, is guaranteed our algorithm [1, 2], whose validity LEFT with massive fermions involved proved a generalization amplitude-operator correspondence. At dimension 8 9, we list 35058 (756) 704584...

To realize first-order electroweak phase transition, it is necessary to generate a barrier in the thermal Higgs potential, which usually triggered by scalar degree of freedom. We instead investigate transition patterns pure fermion extensions standard model, and find that additional fermions with mass hierarchy mixing could develop such strongly models. In potential polynomial parametrization, can be generated following two patterns: (I) positive quadratic term, negative cubic term quartic...

Finding all possible UV resonances of effective operators is an important task in the bottom-up approach field theory. We present tree-level for dimension-5, -6 and -7 Standard Model theory (SMEFT), then obtain correspondence between from relations among their Wilson coefficients, through functional matching operator reduction procedure. This provides a cross-dimension UV/IR dictionary SMEFT at tree-level, methods used here, especially on-shell construction general Lagrangian systematic...

A bstract This is the third of a series works [1, 2] aimed at renormalizing Standard Model effective field theory one loop and to order 1 / Λ 4 , with being new physics cut-off. On this occasion, we concentrate on running two-fermion operators induced by pairs dimension-six interactions. We work mostly off-shell, for which obtain provide explicitly hermitian basis dimension-eight Green’s functions. All our results can be accessed in https://github.com/SMEFT-Dimension8-RGEs .

In the effective field theory (EFT), positivity bound on dim-8 operators tells us that $s^2$ contribution in scattering amplitude of 2-to-2 process geometrically corresponds to convex cone composed ultraviolet (UV) states as external rays. The J-Basis method can provide a complete group decomposition direct product gauge and Lorentz group, thus search for all UV states. Compared previous methods, which only perform groups, greatly improves strictness restrictions also provides systematic...

We construct the on-shell amplitude basis and corresponding effective operators for generic modified gravity theory, such as pure with higher derivatives, scalar-tensor gravity, Einstein-Yang-Mills, etc. Taking Weyl tensor building block, we utilize Young technique to obtain independent operators, without equation of motion total derivative redundancies. update our algorithm vastly increase speed finding monomial (m-basis) expressed in terms tensors Lorentz indices, familiar form General...